Abstract
This section explores some important aspects of the random (stochastic) nature of DEDS and introduces several assumptions that are typically made about it within the model development process.
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Notes
- 1.
This is an example of the statistical notion of an arrival process.
- 2.
Some care is nevertheless required in clarifying which of two possible values is to be taken at the discrete points in time where change occurs. Our convention will be that x(t) = xk for tk ≤ t < tk+1 for k = 0, 1, 2, …
- 3.
The intent here is to circumvent any possible misinterpretation with respect to guidelines (a) and (b).
- 4.
The collection of all values of this output resulting from an experiment, namely, {d1, d2, …, dN} (where N is the total number of messages passing through the network over the course of the observation interval), is an observation of a stochastic process.
- 5.
The notable exception here is the case where a graphical presentation of the data is desired.
- 6.
These two types of study are often referred to as ‘terminating simulations’ and ‘nonterminating simulations’, respectively.
- 7.
Generated using the Microsoft® Office Excel 2003 Application.
- 8.
Source: http://ottawa.weatherstats.ca.
- 9.
The test is shown for the continuous distribution. For discrete distributions, each value in the distribution corresponds to a class interval and pi = P(X = xi).
- 10.
It is also possible to derive the CDF directly from the collected data.
- 11.
The Empirical Class is provided as part of the cern.colt Java package provided by CERN (European Organization for Nuclear Research). See Chap. 5 for some details on using this package.
- 12.
mod is the modulo operator; p mod q yields the remainder when p is divided by q where both p and q are positive integers.
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Birta, L.G., Arbez, G. (2019). DEDS Stochastic Behaviour and Modelling. In: Modelling and Simulation. Simulation Foundations, Methods and Applications. Springer, Cham. https://doi.org/10.1007/978-3-030-18869-6_3
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